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SEQUEL TO 
THE OEIGIN OF THE ST^RS, 

OR 

THE NECESSITY OF NEBULAR ROTATION. 

By J> Ennis. 



Some of the recent discoveries announced in my volume on "the Origin of 
the Stars " have met with objections which could be removed only by the 
statement of new views of the nebular theory and a new dynamical principle. 
This new principle and these new views, being essential to the progress of 
science, I offered for publication in the Proceedings of the Academy of Natural 
Sciences of Philadelphia, and they are contained in the following pages. It 
will now be seen that on the surface of an irregular and contracting nebula 
there may be four different sources of motion, instead of the one mentioned in 
my recent volume. Three of these sources are absolutely necessary, and one 
is* hypothetical. From these several sources of motion there must result a 
single current circulating around the nebulous globe and forming its rotation. 
It will be seen that this current or rotation cannot possibly stop, but that in a 
mass like our solar system its velocity from time to time may equal the velo- 
cities of the several planets. Consequently the centrifugal and centripetal 
forces may become equal, rings may separate from the equatorial zone, and a 
solar system of many members may be created. By following out these views 
with dynamical strictness, every objection usually urged against the nebular 
theory has been answered in my work already named. 

The application of the inclined plane theorem to the nebular hypothesis, I 
regard as the most important step I have made in these investigations ; and 
the two most important fruits of that application are, that gravity is the force 
which gave all their motions to all the stars, and that this discovery affords 
the same support to the nebular theory which the Copernican theory derived 
from the discovery of gravity as the centripetal force. The two cases are quite 
parallel ; and in my 40th Section, p. 326, I have shown that the evidences in 
favor of gravity as the centrifugal or projectile force are equally as strong as 
the evidences in favor of gravity as the centripetal force. 

In the present paper the chief points are : first, the primitive impulses 
through gravity which originate rotation ; secondly, the necessity for a con- 
tinuance and acceleration of that rotation ; thirdly, the distinction, and the 
resemblance between motion in space in the direction of an inclined plane, and 
motion down an actual inclined plane ; and fourthly, that this origin of the 
solar system does not contravene the law of conservation of areas. 

A writer in a New York weekly journal, unknown to myself but described 
by the editor as " an eminent mathematician," thought out and published in- 
dependently the fourth source of motion on the surface of an irregular and 
contracting nebulous mass as given in this paper. Before that time, however, 
this paper, just as it now appears, had been communicated to the Academy, 
but its publication has been delayed unusually long. That source of motion 
was obvious enough after I had developed the idea of a large number of sepa- 
rate irregular contracting nebula, all derived simultaneously from a slow con- 
traction of matter which had been universally diffused. The present powerful 
actions of the fixed stars on one another, first shown in the thirty- seventh 
section of " the Origin of the Stars," also pointed strongly that way. The 
next grand question in advance will be, whence arose that enormous develope- 
ment of the repulsive force which diffused all matter through all space ? 



Extract from the Proceedings of the Academy of Natural Sciences of Philadelphia. 



If matter were universally diffused through all space, the supposition would 
not be in accordance with experience, that this diffusion would be perfectly 
uniform and even. Such is not the result of natural processes in the actual 
world. The waters of the ocean are not perfectly uniform ; their densities be- 
ing varied by temperature and saline ingredients. The air is not uniform, nor 
the vapor of water in the air. Therefore, if matter were universally diffused, 
and contraction were to ensue, then the rarer portions would gather around the 
denser, and the expanded vapor would break up into separate huge irregular 
masses, like the clouds when the vapor of the atmosphere is contracting. 

On the surfaces of these separate nebulous masses we can conceive of four 
sources of motion ; the first only hypothetical, and the other three absolutely 
necessary. 

First source of motion. In this general diffusion of matter, the supposition 
would be unnatural that all was perfectly motionless and still. A state of 
absolute repose might, for aught we know, be possible, but it would be a 
strange and unheard of assumption. How unlikely that the causes which 
spread matter abroad so widely should stop entirely, and leave no motion ! 
Therefore every nebula in its beginning was probably endowed with some 
movements. 

Second source of motion. "When separate nebulous masses were formed by 
the ordinary principles of contraction and condensation, we cannot suppose 
they would be stationed at equal and symmetrical distances from one another, 
any more than we see among the white clouds which float together across the 
dear blue sky, Neither would they be of equal size, for the heavenly bodies, 
like the clouds, are very unequal in size. Therefore, by the force of gravity, 
the smaller would fall into the larger ; and often two or three near together, 
though of similar size, would fall into one another. But any one could never 
fall directly toward the centre of gravity of another ; because every approach- 
ing pair would be more or less under the influence of other neighboring nebu- 
lae. Therefore, in striking each other obliquely, and not in the direction of 
their centres of gravity, a rotation must result. These collisions must have 
been a thousand times more numerous than the fall of meteors now, and so 
they would continue until space became cleared of all small and neighboring 
masses, and nothing remained but large and vastly distant nebulae, each one 
of which is now represented by a great stellar system, containing countless 
numbers of fixed stars. 

Third source of motion. By the assumption of the nebular theory, as under- 
stood by myself, the contraction of a nebula was always much more slow than 
would be due to gravity. Therefore gravity would make the nebula round, 
and the irregular projections, perhaps long arms, would slide down laterally in 
the neighboring depressions. By this process many horizontal currents would 
be produced on the surface. 

Fourth source of motion. These irregular projections, perhaps great ex- 
tended arms but little attached to the nebulae, would be under the influence 



3 

of neighboring nebula similar to tidal influence and stellar perturbation, 
especially while the nebula were still near to one another, though contracting 
steadily to greater distances. Therefore the fall of these irregular prominen- 
ces into the larger mass would be somewhat like the falling together of two 
independent nebula. They would not fall towards the centre of gravity of 
the principal mass, but more or less obliquely, and hence they would lead to 
rotatory motion. 

From these four sources of motion many currents would flow on the surface, 
at least, of every nebula. In those cases where two large nebula fell into each 
other, the currents would pervade the entire mass. But even when the cur- 
rents were superficial only, they could not stop ; because, on account of the 
continued contraction of the nebula, they would flow in the direction of an in- 
clined plane. Witb their horizontal motion they would have an inclined mo- 
tion towards the centre, and gravity would hasten them downward. These cur- 
rents would act and react on one another, and by well known mechanical princi- 
ples they would all result in a single current, as we see by experiment in a basin 
or funnel of water. This one current would be around the centre of gravity, 
and, for the same reason, it could not cease to flow. In consequence of the 
continued contraction of the nebula, every particle of the surface current is 
moving in the direction of an inclined plane, and gravity must give them the 
velocity due to inclined plane motion. If they be retarded by friction on the 
unrotating or slowly rotating interior, then this interior will be moved in the 
same direction, and gravity will carry it onward until the entire nebula ro- 
tates. As the nebula contracts from the extent of its original round form down 
to near its centre, every particle must acquire a velocity equal to that of a fall from 
its original to its last extent, excepting only the retardation due to friction. This 
is one of the most essential ideas in the nebular theory originated by myself, 
and demands a complete illustration. 

Every body approaching toward the centre of the sun, whether directly or 
obliquely, must be hastened by the force of gravity. The celebrated Halley's 
comet, for instance, which requires about seventy-six years to go around its 
orbit, is beyond the distance of Neptune when it reaches its aphelion ; then 
the moment it passes its aphelion, and begins its return toward the sun, it be- 
gins to be hastened on its course by gravity. So it continues to be hastened 
by that force every hour faster and faster, during thirty-eight years. Being 
free to move, and unobstructed, it runs in a conic section, and when it arrives 
at perihelion its velocity has become so great as to have a centrifugal stronger 
than its centripetal force. Therefore it shoots away from the sun again, but 
every hour in its departure its velocity is delayed by gravity. Thus the propo- 
sition is certain that when a body departs from the sun its velocity is retarded, 
and when it approaches the sun its velocity is accelerated, by gravity. Every 
particle in a current on the surface of a contracting nebula is moving oblique- 
ly, like a comet, towards the centre of the nebulous sun, and therefore they 
must all be hurried along by gravity. 

Halley's comet, while descending from aphelion to perihelion, may be re- 
garded as moving down a spiral inclined plane. Its ultimate velocity will be 
the same as if it had fallen to the sun through the height of the plane, plus its 
initial velocity at aphelion. That is, its ultimate velocity will be the same as 



if it had fallen from aphelion in a direct radial line until a distance from the 
sun equal to its periphelion, plus its initial velocity at aphelion. In the same 
manner a particle, while descending in its spiral current towards the centre of 
the nebulous sun, must at any point in its course have the same velocity, fric- 
tion excepted, as if it had fallen in a direct radial line to that point, plus the 
initial velocity which it acquired in the rounding process. I have found by 
calculation that this velocity may be so great as to give all the zone on the 
nebular equator a centrifugal force equal to the centripetal force. Therefore 
a period may arrive in the contraction of a nebula, when the equatorial zone 
can no longer approach towards the centre, but must be abandoned as a ring 
circulating around the nebula, until by perturbation it is broken, and subsides 
by gravity into a rotating nebulous planet. Friction, however, in the cases of 
some nebulae, may be so powerful as to retard the velocity, and prevent the 
separation of matter in the form of a ring. 

There are some points of difference between a comet and a particle on a ro- 
tating equatorial zone. A comet, in departing from the sun, is deprived by 
gravity of all that velocity which, in approaching the sun, was imparted by 
gravity. A nebulous particle does not fly off from the centre like a comet 
when departing from periphelion, because it does not run in a conic section ; 
and it cannot pursue a conic section on account of friction, which retards its 
motion, and also on account of atomic repulsion in the nebulous mass, 
which forces it outside of the elliptic curve on the way towards periphelion. 
The spiral course of the nebulous particle, from the slowness of nebular con- 
traction, is nearly circular, and hence, when the centrifugal equals the centri- 
petal force, the particle takes nearly a circular orbit. Hence, as it always ap- 
proaches the centre of the nebulous mass, it always receives velocity from 
gravity. And when it ceases to approach, it never flies far off, and therefore 
never loses velocity from gravity, as does the comet. 

Gravity could cause no rotation, unless a particle on the surface had first a 
horizontal motion given in the process of rounding the nebula, and unless the 
nebula contracted. By this horizontal motion and by contraction, the particle 
approaches the centre of the nebulous sun obliquely, and gravity hastens it 
down the inclined path. The particle cannot stop, because there is nothing 
to make it stop. Repulsion cannot stop it, because repulsion, like centrifugal 
force, is every instant yielding before it, and allowing it to retain all its actual 
motion, and to acquire more motion by a fall every instant towards the centre.: 
If it be delayed in its velocity by friction on other particles, then just so much 
momentum must be impacted to them, and they too will move in the direction 
of an inclined plane towards the centre, and these again will move other parti- 
cles, and so on until the entire mass moves and rotates. If the particle had 
no horizontal motion, then repulsion and gravity would act upon it in opposite 
directions, and it would partake only of the general contraction in radial lines 
towards the centre. There could be no rotation. But by its horizontal mo- 
tion, and by the slow contraction of the mass, — slower than is due to gravity, 
— the particle finds the path before it every instant settling down. Hence 
every instant it goes down as it goes forward, and its motion is in the direction of 
an inclined plane, and subject to the inclined plane law of increased velocity ; 
that is, a velocity equal to that of a fall through the height of the plane. 



Imagine a circle, the equatorial section of a nebulous globe, with a million 
of radii. Then the particle with a horizontal motion finds at each succeeding 
radius that the surface, by contraction, has gone down towards the centre. It 
must, through gravity, follow that surface downward. Every instant, there- 
fore, it receives a new impulse down its course, — a million of impulses in one 
revolution. Then, with no impulse in the contrary direction, its velocity must 
increase. 

By calculating the velocity of the equatorial zone of our sun down an in- 
clined plane as due to gravity, I ascertained the velocity of rotation of our sun 
when in a nebulous condition, and found that it precisely equalled, at different 
stages of its contraction, the present velocities of the planets and asteroids 
when an infinitessimally small allowance is made for an inevitable friction on 
the unrotating or slowly rotating interior. These small allowances due to 
friction are given in my recent volume, " The Origin of the Stars. ; ' In that 
volume also the rotations of the several nebulous planets are shown to have 
been the same as the present revolutions of their satellites ; and the reason is 
pointed out why the smaller planets could have no satellites. By these and 
by many other coincidences the discovery was first made that Gravity is the 

FORCE WHICH IMPARTED ALL THEIR MOTIONS TO ALL THE STARS. 

It is proper now to attend to three objections which, on account of the pre- 
sent state of astronomical science, naturally rise against this view of the ne- 
cessity and velocity of nebular rotation. 

The first objection is that this view " contravenes the principle of conserva- 
tion of areas." The fallacy of this objection maybe seen by a very simple 
arithmetical calculation. We will take Mercury, whose radius vector moves 
most rapidly, and at the rate of 110,000 per hour. Neptune is about eighty 
times farther from the sun. The original extent of our nebulous sun was half- 
way to the nearest fixed star ; say 3,622 times farther than Neptune, and con- 
sequently, in round numbers, 3622 X 80 = 290,000 times farther than Mercu- 
ry. The area described by the radius vector of Mercury in one hour equals 
that radius multiplied by half its distance per hour, say 1 X 110,000 ~ 2. 
The area described by the radius vector of the original nebulous sun must 
have equalled that radius multiplied by half its distance per hour, say 290,000 
X » —- 2. Both these areas must be equal. Now what must be the value of 
k that, when multiplied by 290,000, gives 110,000 ? Plainly Ji, or £ nearly ; 
that is, the movement of the radius vector of the original nebulous sun, or, in 
other words, its primary rotation, was about one-third of a mile per hour. I 
will soon point out how this velocity was obtained. 

The second objection is drawn from a misapplication of the principle that 
action and reaction are equal, and in opposite directions. By this principle; 
when an object falls to the earth, the earth falls proportionally to the object ; 
when we walk forward in a straight line, we push the earth backward pro- 
portionally ; when a car, by gravity, runs down an inclined plane, the earth 
as well as the plane moves proportionally in the opposite direction : that is 
both upward and backward. Therefore it has been wrongly inferred that when 
a particle, or all the particles, on the rotating exterior of a contracting nebula 
move by gravity in the direction of an inclined plane toward the centre, then 
the interior should move proportionally just the contrary way. It has" been 



6 

wrongly inferred that these two opposite motions should counterbalance each 
other, that in fact there can be no such operation, that the whole idea is like 
" the old absurdity of a perpetual motion, or of a man trying to lift himself up 
by pulling at the straps of his boots.''" 

But all such inferences show a misunderstanding of the case. "We must 
learn to see the difference between moving in the direction of an inclined 
plane, and moving on an actual inclined plane. A comet or a planet approach- 
ing perihelion is moving in the direction of an inclined plane. With its for- 
ward motion in its orbit it has an inclined motion towards the sun, and its 
velocity is hastened by gravity in consequence of this inclination. Imagine a 
hundred comets all in the plane of the sun's equator, and equally distributed 
around the sun, and all approaching their perihelion. While all would be 
accelerated by gravity toward the sun, the sun would not be moved in any 
way towards them, because it would be equally acted on all around by the 
comets. Neither could there be any reaction to make the sun rotate in the 
opposite direction, because there is no actual inclined plane to cause a back- 
ward motion. The comets have the inclined plane motion without an inclined 
plane. In the same manner on the horizontal equatorial zone of a rotating 
and contracting nebula, all the particles move in the direction of an inclined 
plane spirally coiled many times around, and all are hastened by gravity 
according to the law of velocity on such a plane, but not one of them moves 
down an actual inclined plane. They all repose on a level or horizontal 
surface! therefore they do not move the interior backward while they move 
forward. If they were on an actual inclined plane they would create a coun- 
ter movement. But such is not the case. Each one, while approaching the 
centre, draws the entire mass up towards itself, as when a fly alights on the 
earth, but being equally distributed all around, they counteract one anothers' 
efforts in this regard, and produce no result. The reason why there is a back- 
ward reaction on a real inclined plane is simply because of the inclination of 
the surface. An object cannot repose quietly on such a surface. The forward 
motion of the object must give a backward push to the surface. But when 
there is no inclined surface, as on an equatorial zone, there can be nothing 
against which a backward push can be made by mere gravity. 

In its approach toward perihelion a comet is upheld from falling in a straight 
line toward the sun by centrifugal force ; that is, its plane is sustained by 
centrifugal force. In like manner, on the equatorial zone of a rotating and 
contracting nebula, a particle is upheld from falling straight toward the sun's 
centre, partly by centrifugal force and partly by atomic repulsion ; that is, its 
plane is upheld partly by centrifugal force and partly by repulsion. But nei- 
ther of these hinders the force of gravity from imparting every instant an in- 
creased velocity in the inclined plane direction. Both repulsion and centrifu- 
gal force are constantly yielding before the power of gravity, and allowing the 
comet or the particle to be accelerated. In this way inclined plane direction 
and increasing velocity are produced without an actual inclined plane, and 
hence one of the reactions of an inclined plane is wanting : namely, the back- 
ward reaction. The other reaction — the upward — is nullified by opposite 
particles on opposite sides of the nebula. 

Atomic repulsion has two effects different from mere centrifugal force ; it 



hinders the moving particle from following an elliptic orbit, and it causes re- 
tardation by friction. But the direction of its action is always in a radial line, 
always perpendicular to the nebular surface on which the particle quietly re- 
poses ; and it yields every instant like centrifugal force before the power of 
gravity, which continually brings the particle toward the centre. In the be- 
ginning of nebular rotation, and when that rotation is very slow, a particle on 
the exterior presses with nearly all its weight on the interior. It is then up- 
held very little by centrifugal force, and chiefly by repulsion. As it moves 
more rapidly it acquires greater centrifugal force, and presses less heavily on 
the interior. It becomes hourly less and less upheld by repulsion, and more 
and more by centrifugal force. At length it is held up entirely by centrifugal 
force, and presses no more on the interior. It is independent of repulsion ; it 
circulates freely around the centre, without approaching it. The centripetal 
and the centrifugal forces are equal. 

An important illustration may be made with a funnel to show that a fluid 
may move down the direction of an inclined plane without producing the back- 
ward reaction of such a plane. Suspend the funnel by a single small silk braid, 
having no twist. Pour in the water, and give a portion a horizontal motion. 
Give the funnel an equal impulse in the opposite direction. The water, as it 
runs through the funnel, will rotate, and evidently every particle of the water 
will run an inclined plane direction, but the plane must necessarily take the 
form of a coil. According to the principle of the backward reaction on an 
actual inclined plane, the natural expectation would be to see the funnel ro- 
tate in the direction contrary to that of the water. But this does not occur. 
On the other hand, the water, by friction, carries the funnel around in the 
same direction with itself. In like manner the exterior of a nebula must carry 
along the unrotating interior with its own motion. The reason is the same in 
both cases. There is no backward reaction, because in both cases the particles, 
as they move, repose on a horizontal surface. They do not move down an 
actual inclined surface, and hence cannot react according to the law of an in- 
clined plane surface. They have the law of velocity, but not the law of back- 
ward reaction. This absence of the backward, though not of the upward, re- 
action, may be regarded as a new dynamical principle. It has not before been 
detected in the funnel problem, nor in the nebular theory, nor in aught else 
that I am aware. 

The third and last objection is that gravity cannot cause nebular rotation, 
and that it cannot therefore be the force which imparted their present motions 
to : the stars. We have already seen that if, on the surface of the nebula which 
formed our solar system, there had been a movement of rotation only about 
one-third or one-half a mile per hour, then gravity, acting by the law of con- 
servation of areas, would have imparted the velocity of 110,000 miles per hour 
to Mercury. But how could this nebula have received a rotation of half a mile 
per hour? This question is easily answered by following the logical conse- 
quences of the nebular theory, aided by well known facts in astronomy. The 
fixed stars have velocities at least equal to the planets. When they were all in 
a nebulous condition, just broken up from the vast nebulous disk stretching all 
around within the Milky Way, they must have been irregular in form, quite 
near to one another, and endowed with their present rapid velocities. Then, by 



8 

their mutual perturbations, they must have imparted motions to one anothers' 
irregular exteriors. 

The power of perturbation between the fixed stars is much stronger than has 
been suspected by astronomers. In " The Origin of the Stars" I have shown 
that the sun's gravity on Alpha Centauri is now so powerful that that star 
must move more than 2,000 miles per day at right angles to its present direc- 
tion from ourselves, to gain a centrifugal force sufficient to avoid falling into 
the sun. Estimating the masses of the stars from the amounts of their light 
and their distances, then the power of gravity from Alpha Centauri alone on 
our sun is so great that our sun must move more than 5300 miles per day to 
avoid falling into that star ; and for the same reason our sun must fly with a 
velocity of more than 13,000 miles per day to avoid falling into Sirius. When 
these stars were in their nebulous conditions, expanded nearly to one another, 
irregular in shape, and moving past one another with their present astonishing 
velocities, their mutual power for moving currents on their irregular surfaces 
must have been very strong. Moreover, they must have had the same liability 
to fall into one another, and thus to produce rotation as the original stellar 
nebulae. 

We can also readily conceive how, in the very first formation of the several 
solar nebulae, and flying along with inconceivable rapidity, their irregular 
projections may not have had precisely the same motions as the centre of 
gravity. From all these causes we can understand how, after the rounding 
process, a motion of half a mile per hour may have been given to the one re- 
sultant current on their surfaces. 

But whence the proper motions of the fixed stars ? or rather, whence the 
proper motions of the nebulae from which the fixed stars were formed? The 
nebular theory gives the same cause for the forms and the motions of the 
stellar systems as of our solar system. That theory points to a great original 
nebula, whose rotations by the force of gravity formed and moved the ring of 
the Milky Way, and its interior disk, and its scattered exterior clusters. 
Gravity, in causing this rotation and the proper motions of the fixed stars, 
must have acted by the law of conservation of areas ; and now we must in- 
quire how much motion, according to that law, was necessary on the surface 
of our original stellar nebula? If half a mile per hour was sufficient for our 
aolar system, how much was necessary for our stellar system ? On the suppo- 
sition that the stellar motions are as rapid as the planetary, and that the force 
of gravity was equally strong in both, then the original surface motions of 
our solar and stellar nebulae must have been to each other in some proportion 
inversely as the lengths of their radii. But as the length of the stellar radius 
was almost infinitely longer than that of the solar radius, so the original mo- 
tion on the surface of the stellar nebula must have been almost infinitely 
slower than on the surface of the solar nebula ; that is, almost infinitely slow- 
er than half a mile per hour ! 

But whence these very slow motions on the surfaces of the original stellar 
nebulae ? These I have already given in the four sources of motion in the be- 
ginning of this paper. 

In our solar nebula the areas described by the radius vector diminished 
very slowly, on account of the very slight friction, which also retarded th e 
velocities of the planets, as I have shown in Section 19th. 



SEPT. 28 






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